Download Nitrogen Glow Discharge by a DC Virtual Cathode

Nitrogen Glow Discharge by a DC Virtual Cathode
Azza M. Shagera , Amany T. Sroorb, Hoda A. El Tayeba , Hoda A. El Gamala ,
and Mohamed M. Masouda
a
b
Plasma Physics and Nuclear Fusion Department, Atomic Energy Authority, Cairo, Egypt
Faculty of Girls, Ein Shams University, Cairo, Egypt
Reprint requests to M. M. M.; E-mail: [email protected]
Z. Naturforsch. 63a, 412 – 418 (2008); received May 26, 2006
A DC glow discharge operating with a virtual cathode is studied. The system consists of a solid
disc cathode and mesh anode. The discharge occurs in nitrogen gas at the left-hand side of Paschen’s
curve. The plasma electron density in the axial direction has been found to be 0.2 · 108 cm−3 at
2 cm from the mesh. The electron temperature peak value has been found to be 3.5 eV at 6 cm from
the mesh. The radial distribution of the plasma electron density and temperature are discussed. The
variation of the plasma parameters are in good agreement with the experimental results.
Key words: Glow Discharge; DC Virtual Cathode Oscillator; Vircator.
1. Introduction
Normal glow discharges exist at the right-hand side
of Paschen’s curve, and the discharge potential between the electrodes remains constant. The current can
be varied by increasing the number of electrons from
the cathode, which is due to the increase of the discharge area, while the current density is nearly constant. An increase in the current density is required
in order to increase the total current, which will shift
the normal discharge to the up-normal discharge region. In most previous work a virtual cathode oscillator was produced by a pulsed glow discharge plasma
at the left-hand side of Paschen’s curve. The accelerated electron beam crossing the mesh anode interacts
with the formed plasma which generates microwaves.
Many experimental studies have been carried out on
the virtual cathode oscillator (vircator) in order to improve the total current [1 – 6] and to improve emitted
microwave efficiency [7].
The vircator consists of a disk cathode and a mesh
anode, connected to a power supply, which produces
fast high-current pulses to form virtual cathode oscillators for high-power microwave production [8, 9]. Cathodic arcs have a similar construction [10]. A virtual
cathode is formed when the electron beam current in
the drift region exceeds the space charge-limiting current. Although the configuration of the virtual cathode oscillator is simple, the interaction between the
electron beam and the oscillating field is complicated.
The mechanism of the virtual cathode discharge can
be described as follows: The electrons emitted from
the cathode surface are accelerated toward the mesh
anode. The electrons will cross the mesh and form a
virtual cathode where the mean free path for the collisions of the electrons is comparable or larger than the
electrode separation [11]. The virtual cathode prevents
the propagation of beam further downstream. Therefore most of the electrons are back reflected toward the
anode. Only a small fraction of the electrons is allowed
to propagate forward. The forward current increases as
the diode gap increases. This is often called the current leakage [12]. In order to increase the electron energy and to improve the total current, the oscillation
frequency between the real cathode and virtual cathode is increased. The oscillation frequency is optimal
when the plasma frequency coincides with the electron
cyclotron frequency.
In this study the discharge system consists of a solid
disc cathode and a mesh anode similar to the pulsed
virtual cathode oscillators for high-power microwave
production [10, 11] or cathodic arcs but with low DC
voltage and discharge current [10]. The virtual cathode
is expected to be formed in the DC discharge, since the
electron beam current in the drift region exceeds the
space charge-limiting current.
2. Experimental
A virtual cathode DC glow discharge is composed of
two electrodes enclosed by a discharge vessel, which is
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Insulator
Needle valve To
nitrogen
cylinder
Ballon
Electric
probe
413
probe current versus probe voltage and from the electron energy distribution function (EEDF). The electron
density is calculated using the relation
Ies = ne A e(kTe /2π mi )1/2 ,
where ne is the electron density, A the probe’s surface
area, k the Boltzman constant, mi the ion mass, e the
electron charge, and Te the electron temperature.
3. Results
To vacuum system
Discharge electrode
Fig. 1. Schematic diagram of the system.
made of Pyrex glass of 30 cm length and 10 cm diameter, respectively. It contains four ports in the middle of
the vessel for introducing the different diagnostic tools.
The Pyrex vessel was evacuated to a basic pressure of
10−3 Torr. The nitrogen gas was leaked through a needle valve to keep a constant working gas pressure at
10 Torr.
The virtual cathode DC glow discharge consists of a
brass in the form of a mesh, which acts as anode, and of
a copper disc cathode. The anode and cathode are fixed
together by a rod of copper to fix the spacing between
them to 4 mm. The system can move freely in axial
direction through the glass cylinder by moving it up
and down. Figure 1 illustrates the experimental setup.
The cathode is connected to the negative potential of a
DC power supply, which can be adjusted to the desired
voltage, while the anode is connected to the earth.
An electric probe is made from tungsten with a diameter of 0.5 mm and a length of 5 mm. It is inserted
through the port in the middle of the discharge vessel
via a vacuum-sealed system to move freely in the radial
direction. The plasma electron temperature Te is calculated from the slope of the logarithm of the electric
To understand the behaviour of the discharge, the
electrical parameters have been measured. Figure 2
shows the variation of voltage applied between the
mesh anode and the disk cathode and the current
through the system. The figure shows the characteristic
curve of a discharge. The discharge starts at 430 V, and
the corresponding current did not exceed several mA.
It has been found that the discharge current increases
with increasing the potential between the mesh anode
and the disc cathode, according to the relation V ∝ I 3/2 .
Paschen’s curve for nitrogen gas is presented in
Fig. 3; the discharge current is in mA and the separation gap between the electrodes is 4 mm. The relation between the breakdown potential VB and the
pressure factor pd has been presented by von Engel
as VB = C1 (pd)/C2 + ln(pd), where C1 and C2 are
constants, which depend on the type of the working
gas [13].
Fig. 2. Voltage-current characteristic curve.
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Fig. 3. Paschen curve breakdown voltage V versus pd for N2 .
Fig. 5. First derivative dI/dV .
Fig. 4. Characteristic curve of the electric probe.
Fig. 6. Electron energy distribution.
Apparently at higher pd values (above 1.2 Torr
cm) the breakdown voltage between two electrodes
is proportional to pd [14]. Figure 3 shows that the
breakdown potential decreases rapidly with increasing pressure until it reaches its minimum of 325 V at
pd ≈ 1.2 Torr cm. The left-hand side of the curve provides the suitable condition for this experiment, since
the electron-atom collision mean free path is greater
than the electrode separation distance. Hence for pd =
1 Torr cm the virtual cathode will be formed as a result
of the collisions between the electrons and the neutral
atoms outside of the two electrodes.
To measure the plasma parameters such as the electron temperature, the plasma density, and the electron
energy distribution function, which are produced by
the virtual cathode DC glow discharge, a single electric probe is used [15, 16]. In Fig. 4 the electric probe
A. M. Shager et al. · Nitrogen Glow Discharge
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Fig. 7. Axial distribution of the electron temperature.
Fig. 9. Axial distribution of the plasma potential.
Fig. 8. Axial distribution of the electron density.
current Ip is plotted against the applied voltage Vp
to obtain the characteristic curve at an axial distance
z = 6 cm, at r = 0 (at center), pressure p = 10 Torr,
and discharge current 5 mA. Figure 5 shows the dependance of the first derivative dI/dV on the probe
voltage. From this curve we notice that dI/dV increases with increasing probe voltage to reach its maximum value at Vp ≈ 7 V, which is the plasma potential;
then it decreases rapidly to its minimum value ∼ 0, at
Vp ≈ 15 V.
Figure 6 shows the EEDF under the above conditions. The peak temperature turns out to be about 4 eV.
The EEDF curve is similar to the Maxwellian distribution expected from theory. Figure 7 shows the axial distribution of the electron temperature. We observe that it increases along the tube axis z to reach
its highest rate (3.5 eV) at the distance z = 6 cm. At
axial distance more than 6 cm, the electron temperature starts to decrease, which can be attributed to the
weaker electric field and the diffusion of the charged
particles.
The axial distribution of the electron density is illustrated in Figure 8. Note that the electron density increases with axial direction from the mesh to reach its
maximum value 0.2 · 108 cm−3 at z = 2 cm. This may
be due to an increase of the electron beam collisions,
which increases the ionized particles, forming the virtual cathode (negative glow region) around 2 cm from
the mesh. The number of electrons for z larger than
2 cm from the mesh then decreases.
Figure 9 presents the axial distribution of plasma
potential φ obtained from the first derivative of the
probe’s characteristic curve Ip versus Vp at different
axial positions. From the curve we observe that the
plasma potential decreases from the grid anode to
reach its minimum value nearly 15 V at z = 3 cm. The
region near the minimum potential can be defined as
the virtual cathode. Furthermore this figure shows that
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Fig. 10. Axial distribution of the electric field.
Fig. 12. Radial distribution of the electron temperature.
Fig. 11. Axial distribution of the plasma density.
for an axial position of 3 cm from the mesh the plasma
potential increases rapidly, which may represent an expanding plasma column.
The axial electric field (E) distribution has been calculated from the potential (φ ) distribution, E = −grad
φ , as shown in Figure 10. The electric field profile
clearly shows the direction of the electric field if z
is less than 3 cm. We attribute this to the forwardaccelerated electron current. The electric field reverses
its direction after 3 cm. Then it has a nearly constant
and rather low value, which may be interpreted as part
of the backward current.
Fig. 13. Radial distribution of the electron density.
Figure 11 shows the calculated plasma density
dE/dz along the z-axis. From the curve we notice that
the plasma density changes along the tube axis, where
the electric field generated by the beam’s space charge
is related to the electron density by the Poisson equation
∆2 φ = ερ = divE = −d2 φ /d2 z.
Here E is the electric field, ρ the electron density, ε the
permittivity in F m−1 , and z the axial coordinate.
A. M. Shager et al. · Nitrogen Glow Discharge
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with small dispersion, where only the diffusion of the
electron energy toward the discharge wall takes place.
The radial distribution of the electron density is
shown in Figure 13. From this curve we see that
the electron density increases rapidly from the center toward the wall, and reaches its maximum value
2.2 · 108 cm−3 at r = 2.3 cm from the center; then it
decreases.
Figure 14 finally shows the change of the plasma
kinetic energy (nkT ) with radial direction. It is clear
that the kinetic energy increases along the radial
direction to its maximum value at r = 2.5 cm and then
decreases towards the wall. This is due to diffusion to
the wall.
4. Conclusion
The position of the virtual cathode has been estimated to be at about 3 cm from the grid, which can be
confirmed from the change of electric field’s changing
of its direction as well as from the peak plasma density
at that position.
Figure 12 shows the radial distribution of the electron temperature at z = 6 cm, nitrogen gas pressure
p = 10 Torr, and with discharge current I = 5 mA. It
is clear from this figure that the electron temperature
has a maximum value of T = 3.5 eV at the center of
the tube, and it decreases rapidly from the center up to
r ∼ 1.5 cm; then it has a nearly constant level of 1.6 eV
until near the tube wall. This means that the accelerated electron beam is concentrated around the center
A new type of DC glow discharge originating from
a virtual cathode using nitrogen gas has been studied.
The system consists of a disc cathode and a mesh anode. The discharge takes place at the left-hand side of
Paschen’s curve. The plasma electron density in the axial direction has a peak value of ρ = 0.2 · 108 cm−3
at z = 2 cm from the mesh. The electron temperature has a peak value of kTp = 3.5 eV at z = 6 cm
from the mesh. It has been found that the electron
energy has Maxwellian distribution function to good
approximation. The experimental values of the electron density agree with the calculated theoretical one
from the plasma potential (Poisson equation). The
variation of the plasma potential in axial direction
is obtained and the corresponding theoretical plasma
parameters are in good agreement with the experimental results, especially the position of the virtual
cathode.
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